Not sure if this will fix it for you, but, on both computers, take a look inside Internet Explorer.
On the Menu Bar, select Tools > Internet Options and then choose the Connections tab. There are 3 choices you can choose from for internet connections. Give these a look.
One other thing to look at is the dialup connections themselves. See if there is a configuration setting there you can change. I have cable at home and haven't had to mess with DUN settings for quite a while. Then again, I COULD be just getting old!
Randy